sukhman wrote:The infinite sequence Sk is defined as Sk = 10 Sk - 1 + k, for all k > 1. The infinite sequence An is defined as An = 10 An - 1 + (A1 - (n - 1)), for all n > 1. q is the sum of Sk and An. If S1 = 1 and A1 = 9, and if An is positive, what is the maximum value of k + n when the sum of the digits of q is equal to 9? (A) 6 (B) 9 (C) 12 (D) 16 (E) 18

Dear sukman,
With all due respect, they way you have posted this question is virtually incomprehensible, because you are entirely neglecting mathematical grouping symbols. See:
https://magoosh.com/gmat/2013/gmat-quant ... g-symbols/

Here's what I think you are saying:
The infinite sequence Sk is defined as
Sk = 10 S(k - 1) + k, for all k > 1.
The infinite sequence An is defined as
An = 10 A(n - 1) + (A1 - (n - 1)), for all n > 1.
I love sequence problems, but this problem is way too difficult. This is five times harder than anything you would ever conceivably see on the GMAT. Where did you get this problem?
Mike